Stirling's Series and Bernoulli Numbers
From MaRDI portal
Publication:3983930
DOI10.2307/2323860zbMath0743.11012OpenAlexW1991213313MaRDI QIDQ3983930
Dennis M. Rodriguez, Elias Y. Deeba
Publication date: 27 June 1992
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2323860
Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68)
Related Items
Some identities of symmetry for the generalized \(q\)-Euler polynomials ⋮ A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model ⋮ On \(\lambda \)-Changhee-Hermite polynomials ⋮ Two closed forms for the Apostol-Bernoulli polynomials ⋮ Notes on degenerate numbers ⋮ Explicit formulas for degenerate Bernoulli numbers ⋮ Several identities for the generalized Apostol-Bernoulli polynomials ⋮ Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results ⋮ Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\) ⋮ Gamma and Factorial in the Monthly ⋮ On the von Staudt-Clausen theorem for \(q\)-Euler numbers ⋮ Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi poly\-nomials ⋮ Identities of symmetry for \(q\)-Bernoulli polynomials ⋮ Some identities on the \(q\)-Genocchi polynomials of higher-order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\) ⋮ Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials ⋮ An identity of the symmetry for the Frobenius-Euler polynomials associated with the fermionic \(p\)-adic invariant \(q\)-integrals on \({\mathbf Z}_p\) ⋮ Identities of symmetry for higher-order Euler polynomials in three variables. II. ⋮ Symmetryp-adic invariant integral on ℤpfor Bernoulli and Euler polynomials ⋮ Unified Apostol-Bernoulli, Euler and Genocchi polynomials ⋮ Euler numbers and polynomials associated with zeta functions ⋮ Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials ⋮ Some results on power sums and Apostol-type polynomials ⋮ An identity of symmetry for the Bernoulli polynomials ⋮ Degenerate Bernoulli polynomials, generalized factorial sums, and their applications ⋮ Identities of symmetry for generalized Euler polynomials ⋮ A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials ⋮ The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers ⋮ Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under \(S_3\) ⋮ Certain new presentation of the generalized polynomials and numbers ⋮ Identities of symmetry for degenerate Euler polynomials and alternating generalized falling factorial sums ⋮ q-Euler numbers and polynomials associated with p-adic q-integrals ⋮ Unnamed Item ⋮ Alternate Sylvester sums on the Frobenius set ⋮ Unnamed Item ⋮ The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order ⋮ An explicit formula for generalized potential polynomials and its applications ⋮ Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums ⋮ Unnamed Item ⋮ Identities of symmetry for Bernoulli polynomials and power sums ⋮ Symmetry of power sum polynomials and multivariate fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\) ⋮ Unnamed Item ⋮ Unnamed Item